Conservative MPs are seeking to engineer a vote on an EU referendum by tabling an amendment to the Queen's speech next week, expressing regret that the government's legislative programme does not contain a bill introducing a referendum.

The move has the support of hardline Eurosceptics such as John Redwood, Peter Bone, Edward Leigh and David Davis.

It is normal practice for amendments to be tabled to the Queen's speech, but it is for the Speaker to decide whether to accept them. It is likely that the Speaker will accept this amendment, with a vote on Tuesday next week.

It is very unlikely the amendment will be passed, but a sizeable show of Eurosceptic strength would be taken as a sign that David Cameron is struggling to control the mood on his backbenches.

He might have to bring forward his plans to hold a referendum on EU membership one way or another. At present Cameron wants to hold the referendum after he has completed negotiations with his EU partners in the wake of the 2015 general election.

Some Tory MPs either want the referendum at the time of the general election or even in the next two years. An alternative is simply for the government to table a bill to be passed in this parliamentary session enshrining a referendum to be held after 2015.

Earlier on Thursday Nick Clegg, speaking on LBC radio, insisted Britain had to remain in the EU, saying: "I can respect someone who disagrees but nonetheless disagree with them very firmly. So many companies invest in our country precisely because they use the United Kingdom as a launch paid, ie for exports into what is the world's biggest market."

He said it was not possible for people to have their cake and eat it on the EU.

Lord Lamont, another former Tory chancellor, joined the stampede of former Tory cabinet ministers saying it was possible for the UK to survive outside the EU.

Nadine Dorries, the MP who was handed back the Conservative whip only on Wednesday, said she would be joining the rebellion. She said: "People deserve a choice about whether to stay in or out and they deserve it soon. Many of us who talk to our constituents now want the choice to go out and we have to provide it to people."

She said the UK gave £53m a day to the EU and people wanted it kept in the UK to boost growth.

She said: "Europe is failing. It is dying on its feet and it is a very small part of our global opportunity. Instead of looking to a sick and ailing Europe, we should be looking to burgeoning, expanding economic markets in India, Japan and China.

"If David Cameron wanted to shoot Ukip's fox the way to do it is to come out right now and promise the British people a referendum on Europe between now and the next general election. If he did that he would take away the reason for Ukip to exist."

She added: "The local elections have demonstrated that people are concerned about this issue more than people thought."